u=f(r)
计算得到，
r对x的偏导数为rx=x/r

∴u对x的偏导数为
ux=f'(r)·rx=f'(r)·x/r

u对x的二阶偏导数为
uxx=f''(r)·(x/r)²+f'(r)·(r-x·rx)/r²
=f''(r)·(x/r)²+f'(r)·(r²-x²)/r³

同理，
uyy=f''(r)·(y/r)²+f'(r)·(r²-y²)/r³
uzz=f''(r)·(z/r)²+f'(r)·(r²-z²)/r³

所以，
uxx+uyy+uzz
=f''(r)·(x²+y²+z²)/r²+f'(r)·(3r²-x²-y²-z²)/r³
=f''(r)+2/r·f'(r)追问

谢谢啦

你给的答案感觉有点问题追问

恩恩就是这个 谢谢帮忙